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Describe about Arithmetic and Geometric Series?
When the terms of a sequence are added together instead of separated by commas, the sequence becomes a series. You will use series in higher mathematics. Example 1: 3 + 6 + 9 + 12 + ...The pattern is add three to the previous term. When the pattern is to always add or subtract the same number, you have an arithmetic series. Example 2:1 + 2 + 4 + 8 + ...The pattern is multiply two to the previous term. A series that has a pattern of multiplying or dividing by the same number is called a geometric series.
f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1
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The sum of the series 1+1/2+1/4+......is
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